I'd be generally in the if it works it works camp but -

I don't generally like opera singers trying traditional songs if they apply rounded vowels in English to the songs (as they sometimes tend to do). I can think of a few occasions when I heard this when it hasn't worked for me - doesn't mean it never would.

I've heard people from various other countries singing Irish songs and sometimes the pronuncuation has been very bad. Doesn't mean it doesn't work but it also doesn't mean I wouldn't approach the singer afterwards to let them know how they might pronounce the words better. I'd like to think that this would be in an attempt to be helpful rather than snobbery but who knows.

Generally speaking I'd prefer to hear singers sing a song in their own accent than to try to put on the accent of the originating country. I've heard some fairly awful attempts to do the latter and it rarely works well. Having said that I know I uncosciously sing some American or Scotish songs in those accents. Sometimes it sounds better to me that way.

A good tune should sound well on any instrument if played properly. However some tunes are difficult to play on another instrument - some keys are difficult to play on certain instruments.